Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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On the Role Played by Turbulence Closures in Hull Shape Optimatization at Model and Full Scale
On the Role Played by Turbulence Closures in Hull Shape Optimatization at Model and Full Scale
Pages 128-144
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From page 128... ...
Abstract The practical use of automated CFD-based design tools in ship-building industry requires powerful flow solvers, able to take into account realistic geometries as well as complex physical phenomena, such as turbulence. A shape optimization tool is developed in this framework.
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From page 129... ...
In the case of turbulent flows, additional transport equations for modeled variables are solved in a form similar to the momentum equations and they can be discretised and solved using the same principles. Incompressible and non-miscible flow phases are modelized through the use of conservation equations for each volume fraction of phase.
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From page 130... ...
1~. ~ ~ C nb no Figure 1: Arbitrary control volume The various fluxes appearing in the discretised equa tions are built using centered and/or upwind schemes.
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From page 131... ...
kjnkniJ C ey In the above formula, Sij and Wij are the strain rate and the rotation rate tensors respectively: 1 {0Ui bUj ~ sij = - <_ + _J W ~ (bUi bUj) bid is the Reynolds stress anisotropy tensor defined as bid = 2k —3§ij ni is the wall normal vector, and Yw is the wall normal distance.
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From page 132... ...
With fC = 0, the present model is reduced to an eddy-viscosity model even Reynolds stress transport equations are solved to determine k and £. Although this choice is not interesting for turbulence modelization, a first run with fC = 0 can give a good initialization of the Reynolds stress.
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From page 133... ...
technique [22] is used to control the shape perturbations dur- G Mesh update ing the design process.
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From page 134... ...
It may be associated with sophisticated flow solvers, since the solver is considered as a black box, which has not to be modified in order to be included in the design procedure. Furthermore, this approach is less sensitive to the noise, because no information about the derivatives is needed to predict the optimization path, and only moderately converged solutions of the state equations may be used, reducing the calculation costs.
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From page 135... ...
This is why it has been decided to keep such a moderately refined grid, considering the very large amount of computations required by hull shape optimizations. The successful prediction of the hook-shaped mean streamwise velocity contours at the propeller location x/l = 0.485, observed in the experimental measurements, is considered as a key criterion for assessing the performance of turbulence models designed for ship flows.
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From page 136... ...
Actually, during the optimization process, the shape of the hull converges towards a V-shape, and it is well known that such a shape does not produce intense longitudinal vortices, contrary to Ushape. However, the strong dependence of the flow fields with respect to turbulence closures which was observed on the initial shape, is not significantly reduced as long as the sections of the KVLCC2 stern get thinner during the optimization iterations.
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From page 137... ...
As shown in figure 9 and 10, the mean deviation is significantly reduced during the design process, the magnitude of the decrease being 66% at model scale and 72~7o at full scale. One may underline that the mass flux through the propeller disk is slightly increased of some pourcents at the same time.
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From page 138... ...
T Hino, "Shape optimization of practical ship hull forms using navier-stokes analysis," Proceedings of the 7th International Conference on Numerical Ship Hydrodynamics, 1999.
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From page 139... ...
Deng and M Visonneau, "Comparison of explicit algebraic stress models and second-order turbulence closures for steady flows around ships," Proceedings of the Seventh International Conference onNumerical Ship Hydrodynamics, Nantes, France, [21]
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From page 140... ...
Model scale (b) Full scale Figure 12: Drag reduction: shapes at x/1 = 0.44 f initial shape G k-m model O Rij-m model Figure 13: Drag reduction: shapes at x/1 = 0.46 (b)
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From page 141... ...
Model scale (b) Rij—co model Figure 15: Drag reduction: isowalces at full scale \ As initial final ~ \ Ah/ ~ (b)
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From page 142... ...
Model scale initial shape G k-m model (b) Full scale Figure 19: Velocity homogenization: shapes at x/1 = 0.46 ~ ^ k-m model (b)
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From page 143... ...
Initial (b) Final Figure 21: Velocity homogenization: streamlines at full scale (b)
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From page 144... ...
We have done the similar work using CFD tools together with gradient-based optimization techniques to minimize wave drag. We have found that the hull form optimized for a single design speed may yield less desirable hull form for other speeds.
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